For any constant \(c>0\) , we may change coordinates under the contactomorphism \((x_i, y_i, z) \mapsto (cx_i, cy_i, c^2z)\) . This can make either \(a\)  or \(\rho \)  any given size, but not simultaneously. The requirement \(\tfrac{a}{\rho ^2} < 2\)  is the essential condition in the above definition; we claim that every Legendrian \(L\)  contains a Legendrian twist. To show this it suffices to find a contact 3-ball \(B \subseteq Y\)  so that \(B \cap L\)  is a stabilization. Let \(B^3\)  be any small 3-ball intersecting \(L\)  in a single arc. Since \(n > 1\) , the h-principle for isocontact embeddings of positive codimension  [1]} implies that a \(C^0\)  perturbation of \(B^3\)  (fixed near \(L\) ) has the necessary properties.
